Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8q1)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a8q1.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, 23/4}, -z] == (Sqrt[Pi] (15346656950625 + 26191627862400 z + 133339196390400 z^2 - 203183537356800 z^3 + 193508130816000 z^4 + 225173097676800 z^5 + 24018463752192 z^6 + 642097610752 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (5115552316875 + 6392004418800 z - 11930434064640 z^2 + 9977674936320 z^3 + 13807631007744 z^4 + 1493739503616 z^5 + 40080769024 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-15346656950625 - 9821860448400 z - 4031514789120 z^2 + 3259033989120 z^3 + 12805270732800 z^4 + 1464521981952 z^5 + 39879442432 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (265532058107904 z^(19/4))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]